When is vertex painting the right choice to color a model?
Vertex color is faster to setup, and not needing any texture image or UV-unwrapping can be perceived as an advantage in itself. I've helped a colleague setting up his characters for an animation training DVD (cover). He uses mainly vertex color, and not resorting to complex lighting or texture tricks to convey subtly varied colors in each character.

Another project I've been involved in consumes 1.5GB of RAM when rendering, mostly for textures. This one's memory requirement would be orders of magnitude lower.

If your character design needs the detail, then using image/procedural texture would be justified. Otherwise, vertex color can be a viable alternative, especially on computers with less RAM to use.